Integer Constraints and the Integer Optimality Tolerance

Users who solve problems with integer constraints occasionally report that “Solver claims it found an optimal solution, but I manually found an even better solution.” Solver now stops with the message “Solver found an integer solution within tolerance” instead of simply “Solver found a solution,” to highlight the fact that it found a solution within the range of the true integer optimal solution allowed by the Integer Optimality % tolerance in the Solver Options dialog. Since the default setting of the Tolerance option is 1%, Solver will stop when it has found a solution satisfying the integer constraints whose objective is within 1% of the true integer optimal solution. Therefore, you may know of or be able to discover an integer solution that is better than the one found by Solver.

The reason that the default Integer Optimality % tolerance option is 1% is that the solution process for integer problems – which can take a great deal of time in any case – often finds a near-optimal solution (sometimes the optimal solution) relatively quickly, and then spends far more time exhaustively checking other possibilities to find (or verify that it has found) the very best integer solution. The Integer Optimality % default setting is a compromise value that often saves a great deal of time, and still ensures that a solution found by Solver is within 1% of the true optimal solution.

To ensure that Solver finds the true integer optimal solution – possibly at the expense of far more solution time – set the Integer Optimality % tolerance to zero.

 Select the check box to Show trial solutionsin the Solver Options dialog and re-solve. Solver will pause with the message “Solver paused, current solution values displayed on worksheet.” ClickContinue to see the path towards the solution taken by Solver.

Show Solver trial solutions

1. After you define a problem, click Options in the Solver Parameters dialog box.

2. In the Solver Options dialog box, on the All Methods tab, select the Show Iteration Results check box to see the values of each trial solution, and then click OK.

3. In the Solver Parameters dialog box, click Solve.

4. In the Show Trial Solution dialog box, do one of the following:

 To stop the solution process and display the Solver Results dialog box, click Stop.

 To continue the solution process and display the next trial solution, click Continue.

NOTES

 The Show Trial Solution dialog box also appears (only once, not on each Trial Solution) if you press ESC, or if Solver reaches one of the Solving Limits (Max Time, Iterations, Max Subproblems or Max Feasible Solutions) while solving a problem. See Pause or stop Solver.

Pause or stop Solver

If you press ESC while Solver is solving, the Show Trial Solution dialog box appears. Do one of the following:

 Click Stop to stop the solution process. The Solver Results dialog appears with a message that Solver stopped at your request.

 Click Continue to allow Solver to continue solving until you press ESC again, a Solving Limit is reached, or a solution is found.

If Solver reaches one of the Solving Limits (Max Time, Iterations, Max Subproblems or Max Feasible Solutions) while solving a problem, the Show Trial Solution dialog box appears. Do one of the following:

 Click Stop to stop the solution process. The Solver Results dialog appears with a message that the limit was reached.

 Click Continue to allow Solver to continue solving without the limit mentioned in the dialog box message. If another limit is reached, the Show Trial Solution dialog box will re-appear, once for each limit.

NOTES

To set the Solving Limits, see Change Options for All Solving Methods.

To make Solver pause on every Trial Solution, see Show Solver trial solutions.

 Read the topic Problems with Poorly Scaled Models.This is one of the most common causes of unexpected error messages, suboptimal solutions.